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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently. [ABSTRACT FROM AUTHOR]

In this study, we propose two estimators called the 3-step modified maximum likelihood (MML) and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators. [ABSTRACT FROM AUTHOR]

Actuator rate limit phenomenon is ubiquitous in control systems, but it has always been neglected in practical engineering. Especially, few papers are published to investigate the system identification while considering the rate limit. Step function is commonly used in parameter estimation and its first‐order derivative at the step time goes to infinity, which is not affordable by real actuators. As a result, the rate limit slows down the system response speed, misleads the parameter identification, and subsequently affects the controller design and deteriorates the control performance. This study proposes both graphical method and curve fitting method to identify the first‐order plus time‐delay (FOPTD) systems with consideration of the actuator rate limit effect whose limit value is unknown. Quantitative analyses of the parameter mismatch in the traditional FOPTD model and parameter sensitivity analyses are also carried out. Both simulation results and experimental results have shown the necessity and feasibility of defining a new model structure which includes the rate limit value. [ABSTRACT FROM AUTHOR]

This is an extensive tutorial introducing the state of art in Software Reliability Engineering and associated metrics. Software Reliability Engineering (SRE) encompasses many tasks such as Reliability Growth Testing (RGT) based on software reliability growth modeling, assessment of operational reliability, software release time determination and determination of estimated testing time or required testing efforts and resources. The foremost activity in SRE is Software Reliability growth modeling to plan and execute RGT which is carried out as final testing activity in the software development life cycle (SDLC) and is known in different names such as system testing. This phase in SDLC requires extensive use of Computational Mathematics to estimate parameters of the software reliability growth model (SRGM). In this paper, we will briefly discuss the various SRGM parameter estimation methodologies and conclude that the Least Squares methodology provides a satisfactory solution in all situations. [ABSTRACT FROM AUTHOR]

The use of wind as an energy source is becoming popular because of its non-polluting and renewable features. There is an urgent request to develop site-based estimation on wind engineering, which can be used for optimal design of wind turbines and wind farming. The wind speed for Zafarana Project in Suez Gulf, namely Site-3, based on monthly averaged data for 1 year as well as every 10 min for two days, one day in summer season and one day one winter season have been analyzed to estimate the most appropriate method to find Weibull distribution parameters for this site. The investigated methods are the mean wind speed method, the maximum likelihood method, the modified maximum likelihood method, the graphical method and the power density method. These methods results have been compared with the provided data to find their accuracy based on the root mean square errors. From the obtained results, the mean wind speed and the maximum likelihood method are recommended in estimating the wind speed distribution for the studied site in Zafarana wind farm. [ABSTRACT FROM AUTHOR]

Abstract: Increase in refining demand and tighter environmental regulations have led to sharp increases in hydrogen consumption of oil refineries. Hydrogen conservation and effective use are of interest to refineries whose operations and profitability are constrained by hydrogen. Purification is widely used in hydrogen networks of refineries to reduce hydrogen production load. To minimize hydrogen utility consumption, it is necessary to optimize the hydrogen network with purification as a whole. In this paper, for hydrogen purification process, a triangle rule (which can be generalized to polygon rule) is proposed for graphical representation of its mass balance. The proposed procedure treats the product concentration and recovery rate of the purification process as adjustable parameters. An ensuing graphical method is developed for targeting the pinch point and minimum utility consumption of the hydrogen system with purification reuse. This graphical method can be used for any purification devices and in systems with any utility concentration. A refinery case is studied to demonstrate the optimization method. [ABSTRACT FROM AUTHOR]

In this article we consider the problem of testing for parameter changes in ARIMA models based on the cusum test. The proposed test procedure is applicable to testing for the change from stationary models to non stationary models, and vice versa. The idea is to transform the time series via differencing to make the whole time series as a combination of stationary subseries. For this task, we propose a graphical method to identify the right order of differencing. Then the cusum test statistic proposed by Lee et al. (2003) is constructed based the differenced time series. Simulation study and real data analysis are provided for illustration. [ABSTRACT FROM AUTHOR]